Effect of transition metals doping on electronic structure and optical properties of β-Ga2O3

The effects of transition metal (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn) doping on the stability, electronic structure and optical properties of β-Ga2O3 have been studied using GGA and GGA + U. The results show that the U value can correct the strong interaction of the d-layer, causing orbital hybridization and affecting the position and number of impurity energy levels. It can move the conduction band to higher energy levels and weaken the role of Ga-3p in the valence band. The Ti-doped β-Ga2O3 is easily formed, followed by V, Cr, Sc, Fe, Mn, Co, Ni, Cu, and Zn doping. Some bands change regularly with the increase of atomic number. All systems become degraded semiconductors after doping. All doping will make the β-Ga2O3 red shift. Among them, the absorption intensity of Cu doping in the visible light range is significantly improved.


Introduction
β-Ga 2 O 3 has received extensive attention for its property advantages of low cost, unique ultraviolet transmission characteristics, high breakdown electric field strength and so on [1]. Within a few years, a series of researches have been conducted on the physical properties and control methods of β-Ga 2 O 3 , mainly including the electronic structure, optical and magnetic properties of intrinsic β-Ga 2 O 3 and doped β-Ga 2 O 3 [2][3][4][5].
However, the poor conductivity of β-Ga 2 O 3 hinders its application as a transparent conductive oxide (TCO) [6]. It is well known that doping is a useful way to improve the photoelectric properties of materials, including absorptivity, conductivity and mobility. Common doping ions are Si [7], Sn [8], N [9,10], Ce and Al [11]. Some metal ions are also widely doped, such as Ti [12], Cr [13], Cu [14], Mn [15], Fe [16][17][18][19]. Doping with rare earth elements like Eu [20], Tb [21], Tm [22], Er [23], In [24] and Nd [25] can also improve the optoelectronic properties of β-Ga 2 O 3 . Suo et al [26] calculated Sc-Mn doped CdS, it was found that the variation of bandgaps with atomic number. Nevertheless, most studies of doped β-Ga 2 O 3 are based on single or double atoms doping. Researches for the doping atoms are not systematically studied, the variation of the properties for doping material is not obvious. It is difficult to play a good role in guiding experiments.
Furthermore, the generalized gradient approximation (GGA), GGA+U and Heyd-ScuseriaErnzerhof hybrid functional (HSE06) methods [27] were often used to evaluate their influence on the results obtained by computational methods. HSE06 calculation is time-consuming, so some scholars prefer to use the GGA [26]. Because the self-interaction occurs in the GGA method, the theoretical bandgap value is less than the experimental value, so many studies have used GGA+U to calculate the properties of the materials [28][29][30]. However, the setting of U value is different, and the specific function of U value is relatively vague. Little literature investigate the specific role of U value.
Based on the above problems, this paper systematically studies the electronic structure and optical properties of transition metal(TM) elements (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn) doped β-Ga 2 O 3 using GGA and GGA+U methods. It also analyzed the effect of the U value on the electron orbital and the influence of the

Computational details
The monoclinic β-Ga 2 O 3 with C2/m symmetry has a two-fold b rotation axis, which contributes to the movement of free electrons. According to previous studies [15], we considered a 1×2×2 supercell based on monoclinic β-Ga 2 O 3 , which contains 32 Ga atoms and 48 O atoms as shown in figure 1. The lattice parameters of β-Ga 2 O 3 in the experiment are a = 12.23Å, b = 3.04Å, c = 5.80 Å, c/a = 0.474, α = γ = 90°, β = 103.8°. To make the calculation results more authentic and reliable, atomic relaxation was performed on each initial supercell. As shown in table 1, the formation energy of Sc-substituted Ga tetrahedron ( a Sc) is 0.83eV lower than Sc-substituted Ga octahedron ( 8 Sc), which indicates that the Sc-doped tetrahedron( a Sc) is more stable. Hereafter, other doping systems in this article are TM atoms replacing Ga tetrahedra, which are marked as a TM, b TM. Where a TM represents the calculation method is GGA, and b TM represents the calculation method is GGA+U.

Structural characteristics
To analyze the energy stability and feasibility of TM-doped β-Ga 2 O 3 structures, the formation energy E F is calculated by: Here, E F , E d , E P , μ TM , and μ Ga represent the energies of formation, the total energy of the TM-doped system, total energy of the intrinsic β-Ga 2 O 3 , the chemical potential of the doped atom and the chemical potential of the Ga atom, respectively.
The most stable structure is obtained after structural optimization. The optimized lattice constants and formation energies of each system are listed in table 1. It can be seen that the crystal lattice of the doped system has almost no distortion. The principal reason of the microvariation of volume are the difference in ionic radius and the Coulomb repulsion. Comparing the calculated lattice constants with the experimental values of intrinsic β-Ga 2 O 3 , it can be seen that the calculated lattice constants (a=12.49, b=3.09, c=5.89Å) are slightly larger than the experimental values [31] (a = 12.23, b = 3.03 and c = 5.80 Å). The calculation results are in good agreement with the experimental results, which also proves the reliability of the calculation method in this paper. Moreover, the transition metal doped β-Ga 2 O 3 lattice parameters consistent with previous theoretical results [14].
Doping causes small changes in Volume, one of the reasons is the difference in doping ion radius (Ti 2+ 0.90 Å>V 2+ 0.88 Å>Cr 2+ 0.84 Å>Mn 2+ 0.83 Å>Sc 3+ 0.81 Å>Zn 2+ 0.74 Å>Ga 3+ 0.62 Å>Cu + 0.6 Å>Co 2+ 0.58 Å >Ni 2+ 0.56 Å> Fe 3+ 0.55 Å) [26,32,33]. Another important reason is the Coulomb force between ions. Doping will generate excess free electrons and produce Coulomb repulsion or attraction, and the strong effect of Coulomb repulsion will change the volume of intrinsic β-Ga 2 O 3 . For example, the doping radius of Cr 2+ and Mn 2+ is larger than Sc 3+ , but the volume is smaller. Because extra positive charges will appear in the system when Mn 2+ replaced Ga 3+ ions. There is an attraction between the excess positive charge and the free electrons, which leads to a decrease in the energy and volume of the system.
According to the formation energy E F of the TM doping system calculated by the GGA method, it can be concluded that Ti-doped β-Ga 2 O 3 is easier to form in the experiment, followed by V, Cr, Sc, Fe, Mn, Co, Ni, Cu, and Zn doping. Because the chemical potential of Ti atom is the lowest, the highest electronegativity and the greatest attraction to surrounding electrons. Zn-doping is not easily formed, mainly due to the higher chemical potential of Zn atoms, the bonding process needs to release more energy.
Compared with the GGA method, the lattice constants calculated by the GGA+U method is smaller and closer to the experimental value. The trend of lattice constants, volume, and formation energy is consistent with GGA, so this paper will not repeat it. In short, GGA+U will affect the lattice parameters of the system, but does not influence its variation.

Electronic structure
To further discuss why doping affects the photoelectric properties of β-Ga 2 O 3 , and its performance is closely related to the bandgap, the band structure of each system is calculated, as shown in figures 2 and 3. Figure 2 shows the band structure of each TM doping system calculated utilizing the GGA method. Figure 3 shows the band structure of each system calculated by the GGA+U method. It can be seen in figure 2 that intrinsic β-Ga 2 O 3 is a direct bandgap semiconductor, and its conduction band minimum (CBM) and valence band maximum (VBM) are located at the same G point, which is consistent with the literature [14]. when Sc-doped, the bandgap is slightly increased, and the band structure is unchanged. An impurity level is generated below the conduction band, and the conduction band and valence band hardly move when Ti-doped. The impurity energy level produced by Zn doping is at the top of the valence band which could lead to p-type conductivity, and the conduction band valence band has almost no movement, which is consistent with previous studies [34]. However, When V doped, the conduction band (CB) and valence band (VB) of β-Ga 2 O 3 decreased significantly, the Fermi level (E f ) into the CBM. Since the moving speed of VB is slightly faster than CB, the bandgap is slightly increased. Different levels and a certain width of impurity levels are generated in the middle of the bandgap from Ti to Cu doping, which can be designed as an intermediate band material. Because the impurity level can act as a transition state to facilitate electron transition and light absorption. Among them, the valence band and conduction band of V, Cr, Mn doping gradually move upward with the increase of the atomic number, and the bandgap gradually decreases. The valence and conduction bands of Fe, Co, Ni, and Cu doping also move up slowly with the increase of atomic number. In a word, the doping of transition metal elements can introduce impurity levels to improve the light absorption and conductivity of the materials. Some atomic bandgaps show certain regularity with the increase of atomic number. The V, Cr and Fe doping seem to be used as potential n-type dopants. The Mn, Cu and Zn seem to be p-type dopants, which is consistent with some earlier studies [35,36]. As shown in figure 3, the band structure diagram calculated by GGA+U significantly widened the bandgap. The approximate value of the bandgap of β-Ga 2 O 3 under GGA is only 1.949 eV, which is significantly different from the experimental result of 4.9 eV [31]. The GGA+U method was used and the bandgap β-Ga 2 O 3 equivalent was corrected to be about 4.899 eV (see figure 3 b pure), which is very closer to the experimental value. The Fe-doped impurity is at 0.6 eV at the bottom of the conduction band, which approximates the experimental value [17,18]. The impurity level distribution is also slightly different from GGA. On the one hand, U value may have a greater influence on the conduction band, causing it to move towards a higher energy direction. On the other hand, U also affects the position and number of impurity levels. This makes the characteristic as n-type and p-type conductivity inconspicuous. For example, Zn does not cause P-type conduction, which is consistent with the literature [37]. In conclusion, the appropriate range of U does correct the self-action caused by the  insufficient description of Coulomb repulsion at the local Coulomb, so that the bandgap and physical properties are closer to the experimental situation.
In order to further elucidate the characteristics of its electronic structure and explore the reasons for the variation of the bandgap, the density of state (DOS) of each system are calculated as shown in figure 4. Contrast state density diagrams of the two methods can be found that the obvious effect of the U value consists of several sections. First, the peak with the highest energy moves to the lower energy level, and a small peak of O-2s is added next to it. Second, it weakens the role of Ga-3p in the valence band. Then the entire conduction band is moved in the direction of higher energy levels. Finally, it also has a significant effect on the d electrons of doped atoms.
As shown in figure 4, the maximum high-price bandwidth is 7.29 eV, and the Ga-3d state peak is 17.01 eV. Compared with the previous experimental results [37], the electronic structure calculated by the GGA+U method is reasonable. Besides, it can be observed that the conduction band is dominated by the Ga-4s state, and VBM is occupied by the O-2p state from the figure 4(a). Thus, the bandgap of β-Ga 2 O 3 is determined by the O-2p and Ga-4s states, which is consistent with other calculation results [15]. This indicates that there is a p-d orbital hybrid near the conduction band and the valence band. The p-d orbital repulsion mainly acts on VB, which can widen and move upward. The Sc-3d, Ti-3d states major role in the CBM, less impact on the bandgap. The introduction of TM-3d increases the concentration of carriers at CBM, E f is pushed to the high-energy region, and CBM moves downward because electrons obey the Fermi distribution function. Impurity levels are generated after V, Cr, and Mn doping. The O-2p at VM gradually moves to the Fermi level, and the TM-3d and Ga-4s push CM to higher energy levels as the atomic number increases. TM-3d electron is the main component of impurity energy level. More abundant electrons are produced after Fe, Co, Ni and Cu doping, the primary reason is the introduction of d electrons and p-d orbital hybridization. The Zn-3d and O-2p orbitals in the bandgap hybridize to form Zn-doped impurity levels. This is in accordance with the above analyses of energy bands. All in all, TM doping mainly introduced 3d electrons to act on CBM and VBM, and produce impurity energy levels, which leads to changes in the energy band structure. Some bandgaps will change regularly as the atomic number increases.

Analysis of semiconductor degeneracy
To figure out the influence of doping on the conductivity of β-Ga 2 O 3 , the impurity concentration was calculated. According to the knowledge of semiconductor physics, the electronic arrangement no longer obeys the Boltzmann distribution function due to the Poly incompatibility principle and obeys the Fermi distribution when the impurity concentration is greater than 10 18 cm −3 at room temperature. At this time, the semiconductor exhibits a degenerate state [38]. All systems described herein doping concentration of between 7.929×10 22 cm −3 and 8.237×10 22 cm −3 , these systems are degenerate semiconductor. When the system is degenerate state, the impurity energy level at the CBM is conductive, and the donor or acceptor is not fully ionized. Therefore, the ionization energy of the impurity decreases, the metallicity increases, and the bandgap narrow. Further, the effective mass of the carrier after a degenerate semiconductor is relatively small, in favor of the sub-carrier mobility, to improve the conductivity of the system. Briefly, after the semiconductor is degenerate, the conductivity of the system will significantly improve.

Optical Properties
Due to the GGA+U calculation results are more in line with the experimental conditions, only the influence of transition metal doping on the optical properties of β-Ga 2 O 3 using the GGA+U method is studied. Figure 5 is the imaginary part diagram and absorption diagram of the dielectric function of the intrinsic β-Ga 2 O 3 and each doped system and intrinsic system. Figure 4(b3) shows that the optical absorption edge of the intrinsic β-Ga 2 O 3 is 290 nm, which is very close to the experimental value [31]. It can be seen from figure 4(a) that all doping makes the β-Ga 2 O 3 red shift. The red shift is the most obvious after Cu doping, followed by Zn, Co, Fe, Ni, Mn, V, Cr, Ti, and Sc. The phenomenon of red shift is gradually obvious with the increase of the atomic number. Some adjacent atoms may exchange order. Further analysis of figure 4(b) shows that incorporation of the first transition metal element increases the visible light absorption of β-Ga 2 O 3 . After Sc, Ti, V, and Cr doping, the increase of the absorption intensity is not significant. The absorption intensity in the visible light range is significantly stronger after Mn, Fe, Co, Ni, Cu, and Zn doped. Among them, the Cu doped β-Ga 2 O 3 absorption effect is the best. Figure 4(b2) shows that the optical absorption intensity at 400 nm gradually increases with the sequence of Sc<Ti<Cr<V<Co<Mn< Zn<Fe<Ni<Cu. Also, the order of strength will change to some extent due to the different rate of absorption strength weakening at 445 nm, 490 nm, 600 nm, and 700 nm. On account of the absorption strength like Zn will decrease and then increase. In short, Cu is a dopant that can significantly improve absorption in the visible range of β-Ga 2 O 3 compared to the other transition metals, especially Sc and Ti. When Sc ,Ti doped β-Ga 2 O 3 , the impurity level composed of TM-3d state is generated at the CBM, which has little effect on the structure and band gap of the energy band. So the energy required for electrons to transition from the valence band to the conduction band has not reduced, which causes the change of the light absorption is relatively small. The energy band gap increases slightly after Cu doping, but the absorption in the visible light range increases significantly. Because the impurity energy level appears in the middle of the band gap, it acts as a springboard to promote the electronic transition. The impurity level of Cu-3d generated in the band gap reduces the energy required for the transition of VBM electrons to CBM, so the energy of visible light may excite electrons to the CB. Moreover, the repulsive effect between Cu-3d and O-2p reduces the optical band gap width, and the electronic transition of VBM is further facilitated. It is also interesting to note that there is an increase in absorption at the higher energy regions. The absorption of β-Ga 2 O 3 near 32.39eV, 36.41eV, 40.57eV, and 44.42eV was increased by adding Sc, Ti, V, and Cr, respectively. The absorption strength and the bandgap of the doping system go hand in hand. It is worth noting that the bandgap width of Cu is smaller than that of Zn, but the absorption strength of Cu is greater than that of Zn, because the impurity level appears in the bandgap and acts as a springboard to promote the electronic transition after doping with Cu. In conclusion, TM doped β-Ga 2 O 3 is favorable for absorption in the visible and high-energy regions. Cu is an ideal visible light absorption dopant for β-Ga 2 O 3 .

Conclusions
In summary, this paper studies the influence of TM (Sc, Ti, V, Cr, Mn, Fe, Co, Ni Cu and Zn) on the β-Ga 2 O 3 crystal structure, stability, electronic structure and optical properties by using GGA and GGA+U methods. The results show that the lattice constant of each system has little change, the Ti-doped system is more stable, followed by V, Cr, Sc, Fe, Mn, Co, Ni, Cu, and Zn doping system. The U value corrects the strong interaction of the d layer. The primary functions are to move the conduction band to a higher energy level, weaken the role of Ga-3p in the valence band, modify the d electrons of doped atoms to cause orbital hybridization and affect the position and quantity of impurity energy levels. In other words, a suitable range of U does correct the self-action caused by the insufficient description of the local Coulomb exclusion, so that the band gap and physical properties are closer to the experiment.. The TM doping causes 3d electrons to be mainly introduced into CBM and VBM, leading to hybridization of s-p and p-d orbitals, which in turn affects the band structure. Most bandgaps show a certain regularity as the atomic number increases, but the type of bandgap remains unchanged. All systems become degenerate semiconductors after doping, which qualitatively shows that doping can improve the conductivity of β-Ga 2 O 3 . The TM doping makes β-Ga 2 O 3 red-shift and is beneficial to absorption in the visible light range. Among them, Cu-doped β-Ga 2 O 3 has the strongest absorption in the visible light range and is an ideal visible light absorption dopant for β-Ga 2 O 3 .