Defects and Dopants in CaFeSi 2 O 6 : Classical and DFT Simulations

: Calcium (Ca)-bearing minerals are of interest for the design of electrode materials required for rechargeable Ca-ion batteries. Here we use classical simulations to examine defect, dopant and transport properties of CaFeSi 2 O 6 . The formation of Ca-iron (Fe) anti-site defects is found to be the lowest energy process (0.42 eV / defect). The Oxygen and Calcium Frenkel energies are 2.87 eV / defect and 4.96 eV / defect respectively suggesting that these defects are not signiﬁcant especially the Ca Frenkel. Reaction energy for the loss of CaO via CaO Schottky is 2.97 eV / defect suggesting that this process requires moderate temperature. Calculated activation energy of Ca-ion migration in this material is high ( > 4 eV), inferring very slow ionic conductivity. However, we suggest a strategy to introduce additional Ca 2 + ions in the lattice by doping trivalent dopants on the Si site in order to enhance the capacity and ion di ﬀ usion and it is calculated that Al 3 + is the favourable dopant for this process. Formation of Ca vacancies required for the CaO Schottky can be facilitated by doping of gallium (Ga) on the Fe site. The electronic structures of favourable dopants were calculated using density functional theory (DFT).


Introduction
Over the last two decades, great progress has been made in the development of rechargeable lithium (Li)-ion batteries. However, there is a necessity to find alternatives to Li-ion batteries as energy demand increases rapidly with the world population. In this respect, sodium (Na) batteries are currently being considered mainly due to the high abundance of Na [1][2][3][4]. Batteries based on multivalent cations such as magnesium (Mg 2+ ) and zinc (Zn 2+ ) are also promising, as they can provide high energy density [5][6][7][8][9].
A Ca-ion battery is being currently considered as an alternative to Li-ion battery mainly due to the low cost associated with high abundance of Ca and high energy density [10]. However, Ca-ion diffusion is expected to be slow due to its larger ion size compared to that of Li. Furthermore, it is expected that there will be strong attractive or repulsive forces between migrating Ca ions and surrounding ions due to the double positive charge of Ca.
A variety of compounds such as garnets (e.g., Ca 3 Fe 2 Si 3 O 12 ), pyroxenes (e.g., CaMnSi 2 O 6 ), double carbonates (e.g., CaMg(CO 3 ) 2 ), marokites (e.g., CaMn 2 O 4 ) have been tested as cathode materials for application in Ca-ion batteries experimentally or theoretically [11,12]. In a combined experimental and theoretical study on CaMn 2 O 4 by Arryo-de Dompablo et al. [12], it was concluded that deinsertion of Ca ions from CaMn 2 O 4 is hard, and this was further confirmed by the high activation energy (1.00 eV) calculated for the Ca-ion migration. In a DFT (Density Functional Theory) study by Torres et al. [11]

Intrinsic Defect Processes
Point defects in materials are important as they control many physical properties of solids, including diffusion properties and thermodynamic properties. Classical simulations were used to calculate two principle intrinsic point defect energies (vacancies and interstitials). To calculate the Schottky and Frenkel defect processes, energies of point defects were then combined. Anti-site defect in which cations exchange their atomic positons were also calculated. Fourteen intrinsic defect processes were identified, as outlined in Equations (1)- (14) using the Kröger-Vink notation [39].

Intrinsic Defect Processes
Point defects in materials are important as they control many physical properties of solids, including diffusion properties and thermodynamic properties. Classical simulations were used to calculate two principle intrinsic point defect energies (vacancies and interstitials). To calculate the Schottky and Frenkel defect processes, energies of point defects were then combined. Anti-site defect in which cations exchange their atomic positons were also calculated. Fourteen intrinsic defect processes were identified, as outlined in Equations (1)- (14) using the Kröger-Vink notation [39].
FeO Schottky : SiO 2 Schottky : Si X Si  Table 2 reports the defect energies of Frenkel, Schottky and anti-site defect processes. The lowest formation energy is calculated for the Ca-Fe anti-site defect (0.42 eV/defect). This is due to the same charge (+2) of both Ca and Fe. Other anti-site defects (Ca-Fe and Ca-Si) are slightly high due to the charge mismatch. Anti-site defects are common in many oxide materials and have been observed experimentally and theoretically [40][41][42][43]. The O Frenkel (2.87 eV/defect) and CaO Schottky (2.97 eV/defect) energies are close to each other and their energies are lower than the other Frenkel or Schottky energies. However, those defects are not significant at normal temperatures. Both Ca and Fe Frenkel energies are~4.90 eV, suggesting that their formation is unlikely to occur at room temperature. Si Frenkel energy is 9.18 eV/defect inferring the absence of this defect at any conditions.

Calcium Ion Diffusion
To examine the Ca-ion diffusion pathways and their corresponding activation energies, classical simulationes were performed. For a potential high-rate electrode material, ion diffusion with low activation energy of migration is an important factor. The experimental observation of diffusion pathways and their energetics is challenging. In that respect, computational modelling has been useful in providing valuable information on migration pathways and their activation energies [44][45][46][47][48]. We identified two Ca local hops (A and B), as shown in Figure 2. Table 3 reports the Ca-Ca distances and activation energies. In Figure 3, energy profile diagrams for each local hops are shown. Table 3. Ca local hop distances and their activation energies as shown in Figure 3. Calculations show that activation energies are high for both local hops inferring slow diffusion of Ca ions in this material. To construct long-range diffusion pathways, local Ca hops were connected. Two different long-range pathways were identified. The first pathway (A→A→A→A) exhibits a zig-zag pattern in the bc plane with overall activation energy of 4.36 eV. The second pathway consists of local hops B (B→B→B→B) and Ca ions migrate in the ab plane with overall activation energy of 4.49 eV. High activation energies reveal that very slow Ca-ion diffusion would be expected in CaFeSi 2 O 6 . Table 4 reports the activation energies calculated in previous DFT modelling in different Ca-based electrode materials [11,12]. In general, high activation energy is noted. CaMn(SiO 3 ) 2 exhibits a very high activation energy. This should be due to the long Ca-Ca distances. Notably, both CaFeSi 2 O 6 and CaMn(SiO 3 ) 2 have the same crystal structures. Both classical and DFT modelling methods provide similar activation energies for these types of materials.

Migration Path Ca-Ca Separation (Å) Activation Energy (eV)
Energies 2020, 13, 1285 5 of 16 Table 3. Ca local hop distances and their activation energies as shown in Figure 3. Calculations show that activation energies are high for both local hops inferring slow diffusion of Ca ions in this material. To construct long-range diffusion pathways, local Ca hops were connected. Two different long-range pathways were identified. The first pathway (A→A→A→A) exhibits a zigzag pattern in the bc plane with overall activation energy of 4.36 eV. The second pathway consists of local hops B (B→B→B→B) and Ca ions migrate in the ab plane with overall activation energy of 4.49 eV. High activation energies reveal that very slow Ca-ion diffusion would be expected in CaFeSi2O6. Table 4 reports the activation energies calculated in previous DFT modelling in different Ca-based electrode materials [11,12]. In general, high activation energy is noted. CaMn(SiO3)2 exhibits a very high activation energy. This should be due to the long Ca-Ca distances. Notably, both CaFeSi2O6 and CaMn(SiO3)2 have the same crystal structures. Both classical and DFT modelling methods provide similar activation energies for these types of materials.    Energies 2020, 13, 1285 5 of 16 Table 3. Ca local hop distances and their activation energies as shown in Figure 3. Calculations show that activation energies are high for both local hops inferring slow diffusion of Ca ions in this material. To construct long-range diffusion pathways, local Ca hops were connected. Two different long-range pathways were identified. The first pathway (A→A→A→A) exhibits a zigzag pattern in the bc plane with overall activation energy of 4.36 eV. The second pathway consists of local hops B (B→B→B→B) and Ca ions migrate in the ab plane with overall activation energy of 4.49 eV. High activation energies reveal that very slow Ca-ion diffusion would be expected in CaFeSi2O6. Table 4 reports the activation energies calculated in previous DFT modelling in different Ca-based electrode materials [11,12]. In general, high activation energy is noted. CaMn(SiO3)2 exhibits a very high activation energy. This should be due to the long Ca-Ca distances. Notably, both CaFeSi2O6 and CaMn(SiO3)2 have the same crystal structures. Both classical and DFT modelling methods provide similar activation energies for these types of materials.

Solution of Dopants
Performance of an electrode material can be improved by doping aliovalent or isovalent dopants via introducing charge compensating point defects (vacancies and interstitials) in the lattice. Here we investigated the substitution of a range of dopant ions in CaFeSi 2 O 6 using classical simulation to test the most favourable dopants experimentally.

Divalent Dopants
Both Ca and Fe sites were considered for substituion with some divalent cations (M = Ni, Mg, Co, Zn, Mn, Sr and Ba) and the following reaction equations were used to calculate reaction enthalpies. Substitution of divalent cations at the divalent cation sites in the lattice does not require another defect for charge compensation. Figure 4 reports the solution enthalpy as a function of the radius of the dopant ion. The lowest solution enthalpy (0.01 eV) is calculated for Sr 2+ ion at the Ca site (refer to Figure 4a). The ionic radius of Ca 2+ is 1.00 Å. The preference of Sr 2+ can be due to position of both Ca 2+ and Sr 2+ ions in the same group. The second favourable dopant is Mn 2+ with the soultion enthalpy of 0.56 eV and its ionic radius (0.96 Å) is very close to that of Ca 2+ (1.00 Å). Solution enthalpy decreases with the increase of ionic radius from Ni 2+ to Sr 2+ . This is mainly due to the decrease in the cation mismatch. The soution enthalpy of Ba 2+ is 1.03 eV due to its larger ionic radius than that of Ca 2+ .
Exoergic solution enthalpy is calculated for Mn 2+ at the Fe site. The ionic radius of Fe 2+ in an octahedral environment is 0.61 Å. Solution enthalpies for Co 2+ , Ni 2+, Mg 2+ and Zn 2+ are very small and range between 0.02 eV and 0.10 eV meaning that they are also candidate dopants. Both Sr 2+ and Ba 2+ exhibit high solution enthalpies.This is beacause of their larger ionic radii than that of Fe 2+ ion.

Solution of Dopants
Performance of an electrode material can be improved by doping aliovalent or isovalent dopants via introducing charge compensating point defects (vacancies and interstitials) in the lattice. Here we investigated the substitution of a range of dopant ions in CaFeSi2O6 using classical simulation to test the most favourable dopants experimentally.

Divalent Dopants
Both Ca and Fe sites were considered for substituion with some divalent cations (M = Ni, Mg, Co, Zn, Mn, Sr and Ba) and the following reaction equations were used to calculate reaction enthalpies. Substitution of divalent cations at the divalent cation sites in the lattice does not require another defect for charge compensation. Figure 4 reports the solution enthalpy as a function of the radius of the dopant ion. The lowest solution enthalpy (0.01 eV) is calculated for Sr 2+ ion at the Ca site (refer to Figure 4a). The ionic radius of Ca 2+ is 1.00 Å. The preference of Sr 2+ can be due to position of both Ca 2+ and Sr 2+ ions in the same group. The second favourable dopant is Mn 2+ with the soultion enthalpy of 0.56 eV and its ionic radius (0.96 Å) is very close to that of Ca 2+ (1.00 Å). Solution enthalpy decreases with the increase of ionic radius from Ni 2+ to Sr 2+ . This is mainly due to the decrease in the cation mismatch. The soution enthalpy of Ba 2+ is 1.03 eV due to its larger ionic radius than that of Ca 2+ .

MO + Ca → M + CaO
Exoergic solution enthalpy is calculated for Mn 2+ at the Fe site. The ionic radius of Fe 2+ in an octahedral environment is 0.61 Å. Solution enthalpies for Co 2+ , Ni 2+, Mg 2+ and Zn 2+ are very small and range between 0.02 eV and 0.10 eV meaning that they are also candidate dopants. Both Sr 2+ and Ba 2+ exhibit high solution enthalpies.This is beacause of their larger ionic radii than that of Fe 2+ ion.

Trivalent Dopants
Additional Ca 2+ ions can improve its capacity and then enhance ionic conductivity in CaFeSi2O6.
Here we suggest a stratergy to form Ca interstitials by doping trivalent cations (Al, Sc, In, Y, Gd, La and Ga) at the Si site. Previous modelling studies also considered the same strategy in different

Trivalent Dopants
Additional Ca 2+ ions can improve its capacity and then enhance ionic conductivity in CaFeSi 2 O 6 . Here we suggest a stratergy to form Ca interstitials by doping trivalent cations (Al, Sc, In, Y, Gd, La and Ga) at the Si site. Previous modelling studies also considered the same strategy in different battery materials and validity of this stratergy has been confirmed by experimental studies in Li 2 RuO 3 [49]. The solution of M 2 O 3 (R = Al, Sc, In, Y, Gd, La and Ga) was considered using the following reaction (in Kröger-Vink notation).  Figure 5b reports the solution enthalpies calculated using the following reaction equation.
In all cases, solution enthalpies are endothermic, suggesting that a high temperature is required for this process. Current calculations were performed at 0 K and it is anticipated that at high temperature, solution enthalpy values would be less positive. A favourable dopant in this process is Ga. This could be due to the very small difference between ionic radii of Ga 3+ (0.62 Å) and Fe 2+ (0.61 Å). The highest solution enthalpy is calculated for Al 3+ . Both Sc and In exhibit almost similar solution enthalpies deviating only by~0.08 eV from the value calculated for Ga 3+ . From Y to La, solution enthalpies increase gradually with ionic radius.
Energies 2020, 13, 1285 7 of 16 [49]. The solution of M2O3 (R = Al, Sc, In, Y, Gd, La and Ga) was considered using the following reaction (in Kröger-Vink notation ). Figure 5a reports the solution enthalpies of M2O3. The current simulations show that the most favourable dopant is the Al 3+ but the solution enthalpy is highly endothermic. This indicates that the additional Ca can be formed in the form of interstitials into CaFeSi2O6. Experimental verification is needed to determine the exact concentration of the composition. The possible structure of doped compound can be written as CaFeSi2−xAlxO6 (x = 0.0-1.0).
Doping of trivalent dopants at the Fe site can facilitate the formation of Ca vacancies required for the vacancy assisted Ca diffusion and CaO Schottky formation. Figure 5b reports the solution enthalpies calculated using the following reaction equation.
In all cases, solution enthalpies are endothermic, suggesting that a high temperature is required for this process. Current calculations were performed at 0 K and it is anticipated that at high temperature, solution enthalpy values would be less positive. A favourable dopant in this process is Ga. This could be due to the very small difference between ionic radii of Ga 3+ (0.62 Å) and Fe 2+ (0.61 Å). The highest solution enthalpy is calculated for Al 3+ . Both Sc and In exhibit almost similar solution enthalpies deviating only by ~ 0.08 eV from the value calculated for Ga 3+ . From Y to La, solution enthalpies increase gradually with ionic radius. Here we calculate the activation energies for Ca-ion diffusion in the presence of Al 3+ on the Si site. Figure 6 shows the energy profile diagrams for the local Ca hops. Here we calculate the activation energies for Ca-ion diffusion in the presence of Al 3+ on the Si site. Figure 6 shows the energy profile diagrams for the local Ca hops.  Here we calculate the activation energies for Ca-ion diffusion in the presence of Al 3+ on the Si site. Figure 6 shows the energy profile diagrams for the local Ca hops.  Figure 2).
There is a slight reduction (by 0.02 eV) in the activation energy for the local hop A. In the case of hop B, activation energy is reduced by 0.48 eV. In both cases, Ca-Ca distances have been elongated compared to the distances present in the pure crystal structure. This perturbation in the distances can be due to the charge and ionic radius mismatch between Al 3+ and Si 4+ . Our simulation predicts that doping Al on the Si site would not only increase the concentration of Ca 2+ ions in the lattice but also reduces the activation energy of the Ca-ion migration.

Tetravalent Dopants
Here we discuss the results obtained from doping of some tetravalent dopants (Ge 4+ , Ti 4+ , Sn 4+ , Zr 4+ and Ce 4+ ) at the Si site. Solution enthalpy was calculated using the following reaction equation.
Promising dopant for this process is Ge with the lowest solution enthalpy of 0.65 eV (see Figure 7). This is because of the fact that ionic radii of both Ge 4+ (0.39 Å) and Si 4+ (0.40 Å) are very close. Solution enthalpy for the doping of Ti 4+ is 3.20 eV higher by~2.50 eV than that calculated for Ge 4+ . Solution enthalpy increases with ionic radius from Sn to Ce. Solution enthalpy for CeO 2 is 4.19 eV meaning that this highly endoergic process mainly occurs at high temperatures.  Figure 2).
There is a slight reduction (by 0.02 eV) in the activation energy for the local hop A. In the case of hop B, activation energy is reduced by 0.48 eV. In both cases, Ca-Ca distances have been elongated compared to the distances present in the pure crystal structure. This perturbation in the distances can be due to the charge and ionic radius mismatch between Al 3+ and Si 4+ . Our simulation predicts that doping Al on the Si site would not only increase the concentration of Ca 2+ ions in the lattice but also reduces the activation energy of the Ca-ion migration.

Tetravalent Dopants
Here we discuss the results obtained from doping of some tetravalent dopants (Ge 4+ , Ti 4+ , Sn 4+ , Zr 4+ and Ce 4+ ) at the Si site. Solution enthalpy was calculated using the following reaction equation.

MO + Si → M + SiO
Promising dopant for this process is Ge with the lowest solution enthalpy of 0.65 eV (see Figure  7). This is because of the fact that ionic radii of both Ge 4+ (0.39 Å) and Si 4+ (0.40 Å) are very close. Solution enthalpy for the doping of Ti 4+ is 3.20 eV higher by ~ 2.50 eV than that calculated for Ge 4+ . Solution enthalpy increases with ionic radius from Sn to Ce. Solution enthalpy for CeO2 is 4.19 eV meaning that this highly endoergic process mainly occurs at high temperatures.

Electronic Structures of Doped CaFeSi2O6
We employed DFT to examine the electronic structures of defect free and doped-CaFeSi2O6 configurations. The promising dopants were only considered as discussed in the previous sections.
Previous DFT simulations by Streltsov et al. [50] discussed the electronic structure of CaFeSi2O6. Their calculation show that CaFeSi2O6 is a wide gap semiconductor with the band gap of 3.80 eV which is in agreement with the calculated band gap of 3.40 eV in this study (see Figure 8c).

Electronic Structures of Doped CaFeSi 2 O 6
We employed DFT to examine the electronic structures of defect free and doped-CaFeSi 2 O 6 configurations. The promising dopants were only considered as discussed in the previous sections.
Previous DFT simulations by Streltsov et al. [50] discussed the electronic structure of CaFeSi 2 O 6 . Their calculation show that CaFeSi 2 O 6 is a wide gap semiconductor with the band gap of 3.80 eV which is in agreement with the calculated band gap of 3.40 eV in this study (see Figure 8c). Furthermore, the total DOS (density of states) plot shows that there should be a net magnetic moment present as spin-up and spin-down states are not symmetric.
First we considered the electronic structure of Sr substituted at the Ca site in CaFeSi 2 O 6 . The Sr-O bond distances are slightly longer than the Ca-O bond distances. This is due to the larger ionic radius of Sr 2+ (1.26 Å) than that of Ca 2+ (1.00 Å). Fermi energy and band gap were almost unaltered with the doping of Sr (see Figure 8d). However, the states occupied in the gap region sligltly perturbes. Atomic DOS of Sr is shown in Figure 8e. Next we discuss the electronic structure of Mn substituted at the Fe site. Calculated Fe-O and Mn-O bond distances are almost the same. This is due to the similar ionic radius of Fe 2+ (0.61 Å) and Mn 2+ (0.67 Å). Doping of Mn reduces the Fermi energy slightly (by 0.05 eV) and band gap significantly (by 0.80 eV) (see Figure 9).  Doping of Al at the Si site was next considered. Al-O bond distances are slightly longer than Si-O bond distances (see Figure 10). This is due to the larger ionic radius of Al 3+ than that of Si 4+ in a tetrahedral coordination. Fermi energy is shifted by 0.21 eV upon doping. Fermi energy level is occupied by additional states mainly arising from p states of Al (see Figure 10d and e). Substitution of Al at the Si site introduces an electron in the lattice and makes the resultant compound metallic. Doping of Al at the Si site was next considered. Al-O bond distances are slightly longer than Si-O bond distances (see Figure 10). This is due to the larger ionic radius of Al 3+ than that of Si 4+ in a tetrahedral coordination. Fermi energy is shifted by 0.21 eV upon doping. Fermi energy level is occupied by additional states mainly arising from p states of Al (see Figure 10d Calculated bond lengths show that Fe-O bond distances are shorter than the Ga-O bond distances. Ionic radii of both Fe 2+ and Ga 3+ ions are close to each other. However, charge density of Ga 3+ is greater than that of Fe 2+ due to the higher charge (+3) of Ga than that of Fe (+2). Shorter Ga-O bond distances are due to the strong ionic interaction between Ga 3+ and O 2− . Fermi energy increase by 0.35 eV upon Ga doping (see Figure 11). There are no significant peaks arising from Ga near Fermi energy level or in the gap according to the atomic DOS of Ga. However, there is a significant reorientation of spin states and the resultant doped configuration exhibits metallic character. Calculated bond lengths show that Fe-O bond distances are shorter than the Ga-O bond distances. Ionic radii of both Fe 2+ and Ga 3+ ions are close to each other. However, charge density of Ga 3+ is greater than that of Fe 2+ due to the higher charge (+3) of Ga than that of Fe (+2). Shorter Ga-O bond distances are due to the strong ionic interaction between Ga 3+ and O 2− . Fermi energy increase by 0.35 eV upon Ga doping (see Figure 11). There are no significant peaks arising from Ga near Fermi energy level or in the gap according to the atomic DOS of Ga. However, there is a significant reorientation of spin states and the resultant doped configuration exhibits metallic character. Finally, Ge was introduced at the Si site. Though Ge and Si are isovalent atoms, their ionic radii are different (Si 4+ : 0.26 Å and Ge 4+ : 0.39 Å). Larger ionic radius of Ge 4+ reflects in the longer Ge-O bond distances (see Figure 12). Total DOS plot of Ge-doped CaFeSi2O6 is almost unaltered near the Fermi level. This is further confirmed by the atomic DOS of Ge. The Fermi energy is lowered only by 0.08 eV upon Ge substitution. Charge density plot shows that there is a slight perturbation of electron charge density around Fe atoms only. However, charge localization is not observed around the Ge due to the isoelectronic nature of both Si and Ge. Finally, Ge was introduced at the Si site. Though Ge and Si are isovalent atoms, their ionic radii are different (Si 4+ : 0.26 Å and Ge 4+ : 0.39 Å). Larger ionic radius of Ge 4+ reflects in the longer Ge-O bond distances (see Figure 12). Total DOS plot of Ge-doped CaFeSi 2 O 6 is almost unaltered near the Fermi level. This is further confirmed by the atomic DOS of Ge. The Fermi energy is lowered only by 0.08 eV upon Ge substitution. Charge density plot shows that there is a slight perturbation of electron charge density around Fe atoms only. However, charge localization is not observed around the Ge due to the isoelectronic nature of both Si and Ge.

Conclusions
We used computational techniques to provide a detailed atomistic level understanding of key defect processes, diffusion mechanisms and dopant properties in CaFeSi2O6. Calculations show that the Ca-Fe anti-site defect would be dominant in this material. The formation of Frenkel defects is unlikely under normal conditions though the O Frenkel exhibits the lowest Frenkel energy of 2.87 eV/defect. The loss of CaO in this material requires a moderate temperature and can be facilitated by introducing additional Ca vacancies. Ca-ion diffusion in this material is found to be very slow. Doping of Al at the Si site is anticipated to improve the capacity and ion diffusion. Formation of Ca vacancies required for the CaO Schottky can be facilitated by doping Ga at the Fe site. Electronic structure calculations show that CaFeSi2O6 is a wide-gap semiconductor. While isovalent dopants do not affect the electronic structure much, aliovalent dopants alter the electronic structure and gap states.
Author Contributions: Computation, N.K.; Writing, N.K.; Analysis and Editing, A.C. All authors have read and agreed to the published version of the manuscript.

Conclusions
We used computational techniques to provide a detailed atomistic level understanding of key defect processes, diffusion mechanisms and dopant properties in CaFeSi 2 O 6 . Calculations show that the Ca-Fe anti-site defect would be dominant in this material. The formation of Frenkel defects is unlikely under normal conditions though the O Frenkel exhibits the lowest Frenkel energy of 2.87 eV/defect. The loss of CaO in this material requires a moderate temperature and can be facilitated by introducing additional Ca vacancies. Ca-ion diffusion in this material is found to be very slow. Doping of Al at the Si site is anticipated to improve the capacity and ion diffusion. Formation of Ca vacancies required for the CaO Schottky can be facilitated by doping Ga at the Fe site. Electronic structure calculations show that CaFeSi 2 O 6 is a wide-gap semiconductor. While isovalent dopants do not affect the electronic structure much, aliovalent dopants alter the electronic structure and gap states.
Author Contributions: Computation, N.K.; Writing, N.K.; Analysis and Editing, A.C. All authors have read and agreed to the published version of the manuscript.