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(1.School of Information Science and Engineering, University of Jinan, Jinan 250022, China;2.Shandong Provincial Key Laboratory of Network Based Intelligent Computing, Jinan 250022, China;3.School of Information and Electrical Engineering, Ludong University, Yantai 264025, China)

Abstract:The structural, electronic and optical properties of Mg single doped, N single doped and different concentrations Mg-N co-doped β-Ga2O3 were studied via the first-principles calculation based on density function theory. This work aims to improve the effect of p-type β-Ga2O3doping. Five models were built including Mg single doped, N-single doped, 1 Mg-N doped, 2 Mg-N doped and 3 Mg-N doped β-Ga2O3. Among them, the model of 3 Mg-N doped β-Ga2O3 shows the most stable structure than other doped systems. In attention to, the bandgap of 3 Mg-N doped β-Ga2O3 material is the smallest. And occupied states contributed by N 2p and Mg 3s inhibit the formation of oxygen vacancies, which increases the concentration of holes. Thus, 3 Mg-N doped β-Ga2O3 system displays excellent p-type feature. Adsorption peak is obvious red-shift in 3 Mg-N doped system, and the adsorption coefficient is bigger at solar-blind region, which is ascribed to the interband electron transition from the Ga 4s, Ga 4p, Mg 3s of conduct band to O 2p, N 2p of valence band. This work will provide a theoretical guide for the study and application of p-type β-Ga2O3 materials.

Key words:β-Ga2O3; doping; p-type doping; structural property; electronic property; optical property; first-principle

0 Introduction

Ga2O3has excellent physical and chemical properties including wide band gap of ～4.9 eV, high breakdown filed of ～8 MV·cm-1, low loss, high power capacity, faster electron drift, good thermal and chemical stability, which has attracted much attention for the widely application ranged from civil to military aspects[1-5]. For example, Ga2O3is a potential candidate for next-generation high-power semiconductor devices such as Schottky barrier diode (SBD)[6-8], metal-oxide-semiconductor field-effect transistor (MOSFET)[9-10]and solar-blind detector[11-12]. It is found that β-Ga2O3shows the best characters among six different phases[13], so β-Ga2O3is mainly researched in this paper. In recent years, the doping of β-Ga2O3has been a hot point due to the low carrier concentration in intrinsic semiconductor. According to experiments and calculation, doping with appropriate elements can improve the electronic properties and optical properties of intrinsic semiconductor. In the case of n-type doping, the performance has been greatly improved by the doping of Sn, Si and H[14-18]. However, the p-type doping is still faced with enormous challenges. In present, the group 1, 2 and 5 like Li, Mg, Zn, Cu and N[19-22]has been studied by experimental and theoretical method. Kyrtsos et al[23]reveals that Mg-doped Ga2O3forms shallower acceptor level in comparison with other dopants. And Mg is the most stable acceptor species which has been confirmed by Lyons et al and Tang et al. What’s more, solar-blind ultraviolet photodetector based on Mg-doped p-type β-Ga2O3has been achieved[24]. The N-doped p-type β-Ga2O3also was fabricated in 2010[25]. Subsequently, Zhang et al[26]and Dan et al[27]indicates that N-doping is a very promising method to get p-type β-Ga2O3using the first-principles calculation.

What effect will be generated if the acceptor Mg atom and donor N atom are doped together in β-Ga2O3crystal? In recent years, the co-doped method obtains critical achievements on the improvement of oxide material properties, such as Y-Cu co-doped ZnO[28], Zn-N and Mg-Zn co-doped β-Ga2O3[29-30]. On basis of above states, Mg single-doped, N single-doped and Mg-N co-doped models with different concentration were built to investigate the effect of doping Mg, N atom on structural properties, electronic properties and optical properties of β-Ga2O3supercell from theoretical calculation. The results may make profound different on producing p-type β-Ga2O3photoelectric devices.

1 Computational section

β-Ga2O3belongs to space groupC2/m, which has two different Ga sites, denoted as Ga(1) and Ga(2), and three different O sites, denoted as O(1),O(2) and O(3)[31-33]. As Fig.1(a), (b) shown, the monoclinic gallium oxide (β-Ga2O3) and 1×2×2 β-Ga2O3supercell is built and the various sites of Ga, O are labeled.

Fig.1 (a) The cell of β-Ga2O3; (b) (1×2×2) β-Ga2O3 supercell

The Ga(1) atoms is bonded to four O atoms called distorted tetrahedon and Ga(2) atoms are surrounded by six O atoms in the form of a distorted octahedra. O(1) and O(2) are threefold coordinated, while O(3) is fourfold coordinated. According to a lot of researches, the structure is the most stable when N atom substitutes O(2) and Mg atom replaces Ga(2). So in this paper, the model of Mg single-doped, N single-doped and Mg-N co-doped with different concentration is shown in Fig.2(a), (b), (c), (d), (e) and (f). The structures of Mg-N co-doped with different concentration are built which includes 1 Mg-N, 2 Mg-N and 3 Mg-N. They are called 1-dopedMg-N, 2-dopedMg-Nand 3-dopedMg-N, respectively.

Fig.2 5 different models. (a) Mg single-doped; (b) N single-doped; (c) 1-dopedMg-N; (d) 2-dopedMg-N; (e) 3-dopedMg-N

Formation energy, electronic properties and optical properties were calculated by the CASTEP program code in Materials Studio (MS). Due to the defect of the generalized gradient approximation (GGA), GGA+U method was used to calculate band gap in this work. By several tests, the value of p and d orbits is set to 5.50 eV and 5.80 eV in Electronic Configuration of Hubbard U. The energy cut-off is set as 570 eV. The special K points of 2×8×4 Monkorst-parks are summed in all Brillouin zones in reciprocal space. The convergence tolerances are set as follows: the total energy within 2×10-5eV/atom, Hellmann-Feynman force less than 5×10-2eV/nm, maximum stress and displacement are 0.1 GPa and 2×10-4nm. The valence electron configurations of Ga(3d104s24p1), O(2s22p4), Mg(3s2) and N(2s22p3) were treated in this work.

2 Results and discussion

2.1 Structural properties

The geometry optimization was carried with GGA method, all undoped and doped structures are stable. The optimized structure parameters of β-Ga2O3and doped β-Ga2O3are listed in Table 1. For the cell of β-Ga2O3, the values demonstrate the agreement between calculated and experiment results. The doped systems have bigger lattice constant and volume in comparison with undoped crystal. The reason is that the radius of Mg(136 pm) and N(70 pm) atom is bigger than Ga(126 pm) and O(66 pm) atom. The relative stability of Mg single-doped, N single-doped and Mg-N co-doped with different concentration were compared by calculating the formation energy based on the following formulas:

Ef1=EMg-doped-Eundoped+n1μGa(2)-n1μMg

(1)

Ef2=EN-doped-Eundoped+n2μO(2)-n2μN(yùn)

(2)

Ef3=Edoped-EMg-N co-doped+n1μGa(2)-n1μMg+n2μO(2)-n2μMg

(3)

WhereEf1,Ef2,Ef3are the formation energy of Mg single-doped, N single-doped and Mg-N co-doped with different concentration.EMg-dopedrepresents the energy under Mg doping conditions.EN-dopedrepresents the energy under N doping conditions.EMg-N co-dopedrepresents the energy under Mg-N co-doping conditions.Eundopedrefers to the energy of 1×2×2 β-Ga2O3supercell.n1indicates the number of replaced Ga atom.μGa(2) is the chemical potential of one replaced Ga atom.n2is the number of replaced O atom.μO(2) stands the chemical potential of one replaced O atom.μMg stands the chemical potential of one replaced Mg atom.μN(yùn) stands the chemical potential of one replaced N atom. The calculated formation energy of Mg single-doped, N single-doped and Mg-N co-doped with different concentration is collected in Table 1.

Table 1 The lattice constant, volume and formation energy of Mg single-doped, N single-doped and Mg-N co-doped with different concentrations

Obviously, all doped systems display negative values signifying the formation of doped systems are exothermic and spontaneous. For single-doped, the N single-doped system is -6.62 eV and Mg single-doped system is -4.47 eV, which illustrates N single-doped system is more stable in comparison with Mg single-doped system. On the other thing, the Mg-N co-doped with high concentration has higher formation energy indicating co-doped structure prefers to heavy doping. Moreover, the Mg-N co-doped exhibits great stability in contrast with monotonical doped. As above discussed, the Mg-N co-doped with high concentration shows more stable structure.

2.2 Electronic properties

The energy band and density of states were calculated to analyze the electronic properties of doped structure. The Femi energy is set to 0 eV. As we all know, the GGA method tends to underestimate the band gap because DFT theory is based on the ground state theory. In order to the accuracy of results, the GGA+U method was utilized. As Fig.3 illustrated, the band gap of undoped 1×2×2 β-Ga2O3supercell is 4.906 eV, which is closed to experiment value[1]. So the reasonability of this method is confirmed.

Fig.3 The band structure of (a) 1×2×2 β-Ga2O3 supercell, (b) Mg single-doped, (c) N single-doped, (d)1-dopedMg-N,(e) 2-dopedMg-N, (f) 3-dopedMg-N β-Ga2O3

To observe clearly the contribution of the atomic orbitals from doped systems, the partial density of states(PDOS) for the Mg single-doped, N single-doped and 3-dopedMg-Nwere calculated and the corresponding results are exhibited in Fig.4(a), (b) and (c). The dotted line represents Femi energy.

Fig.4 PDOS of (a) Mg single-doped β-Ga2O3; (b) N single-doped β-Ga2O3; (c) 3-dopedMg-N β-Ga2O3

In the case of Fig.4(a) and (b), the electron states of valence band are all consisted by O 2p, O 2s, Ga 3d and N 2p, and the O 2p is related to the flatness of valence band. This result is agreed with band structure. Additionally, it is found that the bowing of conduct band minimum is bigger than valence band maximum based on band structure. The reason is that the conduct band minimum is determined by the hybridization between s and p states. For example, Ga 4s, Ga 4p, O 2p are main part in N-doped system. Besides, the Mg-doped structure includes Ga 4s, Ga 4p, O 2p. There are electron states of Ga 4s, Ga 4p, O 2p, Mg 3s, N 2p in 3-dopedMg-Nsystem. However, valence band maximum is only composed by 2p state of different atoms, which means that the hybridization of p state is the main factor to determine the VBM. It is acknowledged that the energy difference of p state is smaller than s state[36]. Generally, the smaller the energy difference, the smaller the band bowing. As the above analysis, it can be deduced that the bowing of CBM should be bigger than that of the VBM. In Fig.4(b), it can see that there are new electron states from 0 eV to 3 eV due to the doping of N impure, which leads to intensive energy states under Femi level in band structure. According to Fig.4(c), the upper of valence band composed primarily O 2p, Mg 3 s and N 2p. It is worthy to note that the orbit of N 2p through Femi energy. Due to the co-work of Mg 3s and N 2p atom, the effect of O 2p is restrained, corresponding to the fluctuation of valence band. P-type feature of 3-dopedMg-Nβ-Ga2O3is attributed to above results.

2.3 Optical properties

As the material of photoelectric devices, the optical properties including dielectric function, adsorption, reflectivity coefficient and loss function are significant parameters to predict the feasibility of doped β-Ga2O3. Those systems of Mg single-doped, N single-doped, 1-dopedMg-N,2-dopedMg-Nand 3-dopedMg-Nβ-Ga2O3were calculated. In Fig.5(a), the dielectric function describes a close relationship between photons and electrons, which can be calculated according to the following formula:ε(ω)=ε1(ω)+iε2(ω).Whereωis the angular frequency,ε1andε2is the real part and imaginary part of dielectric function.ε2(ω) is thought of as the real transition between occupied electronic states and unoccupied electronic states and can be obtained directly from the CASTEP code;ε1(ω) can be evaluated from imaginary partε2(ω) through the Kramer-Kronig relationship[37].

(4)

(5)

Whereε0stands for the vacuum dielectric constant,manderepresent the electron mass and electron charge respectively,ωis the angular frequency,CandVrepresent the conduction band and valence band respectively, andEC(K),EV(K) are the intrinsic level of the conduction band and valence band. BZ is the first Brillouin zone,Krepresents the electron wave vector,ais the unit vector of the vector potential A, andMV,Cis the unit of transition matrix.

Only the imaginary part of dielectric function sinceε2(ω) depicted the energy required for the transition of the electron from the valence band and conduct band was analyzed. In Fig.5(a), imaginary part of dielectric function shows the value of 3-dopedMg-Nβ-Ga2O3is bigger between 4.5 eV and 6.2 eV than other models, which originates from the interband electron transition between the Ga 4s, Ga 4p, Mg 3s of conduct band and O 2p, N 2p of valence band according to PDOS.

Fig.5 (a) The imaginary part of dielectric function of Mg single-doped, N single-doped, 1-dopedMg-N, 2-dopedMg-N, 3-dopedMg-N β-Ga2O3; (b) the real part of dielectric function of Mg single-doped, N single-doped, 1-dopedMg-N, 2-dopedMg-N, 3-dopedMg-N β-Ga2O3

The adsorption coefficient can be calculated by equation (6):

(6)

Whereε1andε2are the real part and imaginary part of dielectric function,α(ω) is absorption coefficient.

The results are displayed in Fig.6. For Mg single-doped and N single-doped, the trend of curve is similar, and the peak of N single-doped is bigger, which is considered that N 2p makes more contribution to electron transition compared with Mg 3s. For 3-dopedMg-Nβ-Ga2O3, it is clearly perceived that the major adsorption peak shifts to low energy region, by comparison, named red-shift phenomenon as the co-doping of Mg and N atoms leads to a reduction in the forbidden band gap. After the heavy doping of Mg, N atoms, the adsorption coefficient more rapidly increases at 5.96 eV(208 nm) than Mg single-doped and N single-doped systems, signifying the system of 3-dopedMg-Nβ-Ga2O3has excellent solar blind feature. Those results demonstrate 3-dopedMg-Nβ-Ga2O3preforms great optical properties in solar-blind area.

Fig.6 Adsorption of Mg single-doped, N single-doped, 1-dopedMg-N, 2-dopedMg-N, 3-dopedMg-N β-Ga2O3

The formula of reflectivity coefficient is expressed as:

(7)

WhereR(ω) is absorption coefficient.

The change of reflectivity in different doped structures is observed in Fig.7. 3-dopedMg-Nβ-Ga2O3has the most obvious variation in this case. After heavily co-doping, the main peak moves toward the low energy region. And in the 20 eV to 40 eV high energy region, the doped system shows decreased reflectivity, which implies that the ability to transmit in ultraviolet region is significantly increased.

Fig.7 Reflectivity of Mg single-doped, N single-doped, 1-dopedMg-N, 2-dopedMg-N, 3-dopedMg-N β-Ga2O3

3 Conclusion

As above discussed, the structural properties, electronic structure and optical properties of Mg single-doped, N single-doped and Mg-N co-doped β-Ga2O3with different concentration were investigated using the first-principles based on DFT. In this work, the results of formation energy suggest that co-doped system possesses more stable condition than single-doped and the system is inclined to heavily co-doping. The band gap of undoped β-Ga2O3was determined as 4.906 using GGA+U, which is closed to the experiment result. After doping, the bandgap becomes smaller, especially, the 3-dopedMg-Nβ-Ga2O3greatly reduces. According to PDOS, the doping of Mg and N atoms inhibit the effect of O vacancy, improving the mobility of hole. And the electron state around Femi level makes it easy to conduct electricity, namely, intensive metal properties. Most important, the heavily doping of Mg and N atoms shows obvious p-type feature. This result demonstrates that the co-doping of acceptor and donor has critical influence on p-type conductivity. The dielectric imaginary part of 3-dopedMg-Nβ-Ga2O3is larger than other doped system in solar-blind area. Adsorption peak of 3-dopedMg-Nβ-Ga2O3exhibits red-shift against other doped systems dues to the interband electron transition between the Ga 4s, Ga 4p, Mg 3s of conduct band and O 2p, N 2p of valence band. This work has critical guiding significance on the p-type β-Ga2O3solar-blind photoelectric devices.